Competitive Equilibria of Economies with a Continuum of Consumers and Aggregate Shocks

This paper studies competitive equilibria of a production economy with aggregate productivity shocks. There is a continuum of consumers who face borrowing constraints and individual labor endowment shocks. The dynamic economy is described in terms of sequences of aggregate distributions. The existence of sequential competitive equilibria is proven and a recursive characterization is established. In particular, it is shown that for any sequential competitive equilibrium, there exists a payoff equivalent sequential competitive equilibrium that is generated by a suitably defined recursive equilibrium with state variables including continuation value.